# George Van Eps says there are 364 million note combinations, but I can't compute this number

Someone told me George Van Eps computed the number of chord combinations in his book “Harmonic Mechanisms for Guitar” and it came out to 364 million chord possibilities. I found that Ted Greene made a reference to it in an interview with GVE linked below, but it is only mentioned in passing.

I attempted some of my own calculations, but it misses the mark. I even tried if Greene confused million with billion.

If I assume 24 frets on a 6-string guitar, plus open strings and muted strings adding two more notes, it should be 26^6 = 308,915,776 = 308 million.

If I assume the result should be 364 billion, on an 8-string guitar you might calculate 26^8 = 208,827,064,576 which is around 209 billion.

So none of these results suggests 364 million or 364 billion.

I'm not sure if what he had in mind was specific to the guitar or not, but he wrote books for 6-string guitar and played a 7-string guitar himself.

Can anyone elaborate on how GVE came up with the figure?

I also got this idea about how many melodies you can make out of n notes from here https://plus.maths.org/content/how-many-melodies-are-there

The formula is

f(n) = 13^n-(13-1)^n

If we use an octave we have 8 notes out of a possible 13.

f(8) = 13^8-(12)^8 = 385,749,025 = 386 million

I think this is the closest I can get to the suggested 364 million possibilities.

• Have you read the original book? Maybe he explains the calculations Commented Dec 1, 2019 at 9:55
• If you are looking at all combinations - i.e including those with just two or three notes sounding - then isn't there the added complication of double counting? There must be quite a few two, three and four note chords that can be done in more than one way. Doesn't help I know but I was just wondering.
– JimM
Commented Dec 1, 2019 at 10:19
• Heading says 'note combinations', text says 'chord combinations'. Very different from each other.
– Tim
Commented Dec 1, 2019 at 10:29
• Yes, I'm interpreting it as note combinations, but the person who told me about the combinations said chord combinations. They are related, so it depends what you mean, however, I think they are virtually synonymous. The difference between starting with 3 notes for a chord, or 1 notes is not large in terms of whatever combinations you want to achieve when we are talking of to the power of x. What I'm trying to do is get very close - say within one or two million, because that could just be a rounding error. Commented Dec 1, 2019 at 10:45

I found a post on a guitar message board that quotes a calculation from the book (Volume 1, page 17, "General Remarks - Selectivity").

The quote describes:

• The number of permutations of the 6 open strings is 6! = 720.

• The number of permutations of the 12 chromatic tones is 12! = 479,001,600.

• Then -- I don't understand why -- these two amounts are multiplied together to get 344,881,152,000.

Unless there is another calculation in the book, this is probably the number being referred to in the interview.

• While I do think you have an answer to the GVE number, it really doesn't make sense. Permuting the 6 strings does not give you a new chord. Or does it? Can you explain?
– user50691
Commented Dec 2, 2019 at 22:39
• @ggcg It doesn't make sense to me either: 6! represents permutations of the open strings. 12! represents permutations of chromatic tones. But I can't think of anything represented by multiplying them together. Be aware that the quoted passage doesn't mention chords at all. I guess people who read the book probably told their friends it was the number of "possible chords" or number of "note combinations" because the original passage is vague about what the number actually represents. Commented Dec 3, 2019 at 5:04
• I agree and think its probably a red herring
– user50691
Commented Dec 3, 2019 at 11:46

Maybe George was a better jazz guitarist than mathematician?

(Edit) There are other factors that could easily throw such a calculation one way or other by 10 or 20% ...

• how large are the player's hands?
• how many frets has the guitar in question, and how many are actually reachable?
• is any combination of two or more notes considered a "chord"?

I wouldn't personally spend any amount of time trying to reach the exact same conclusion GVE did.

• This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review Commented Dec 2, 2019 at 10:12
• It does not provide an answer but it does provide a very conceivable explanation as to why the OP might be having difficulty. Commented Dec 2, 2019 at 10:18
• @TimH, The question may be a red herring. GVE may simply be wrong. And I think this answer points that out implicitly. I'd recommend the author enhance the answer with this point.
– user50691
Commented Dec 2, 2019 at 22:41
• Yes, I think you are all correct. And that danmcb's answer actually was a relevant answer. After the edit it definitely is. Commented Dec 3, 2019 at 8:09
• yes the original was a little curt. Thank you for your suggestions. Commented Dec 3, 2019 at 8:43